Is there any answer for an incoming anti-carrier missile?
Yes. The Raytheon RIM-116 Rolling Airframe Missile.
Standard Missile (SM) is the most common present system as the outer ring missile.
Next is the Sea Sparrow / Rolling Frame missile
5” Gun with advanced Proxiemty fuse and Phalanx / CWIS with Hyper Vel rocket system and 20 or 30 mm Rotary Cannon.
Some use of low power laser to “dazzle” optical guided system has been tried.
US Navy probably will field first EM-Rail Guns soon.
http://breakingdefense.com/2014/04/navys-magnetic-super-gun-to-make-mach-7-shots-at-sea-in-2016-adm-greenert/
US Army and Navy are looking at a 155mm / 5” gun round at high vel with both anti aircraft and anti missile capabilities, but in the most nascent of stages